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# Confused by exponents of i

We are asked the question what is i^100. The answer is 1 because i^4 = 1 and i^100 can be rewritten as (i^4)^25.

But can't it also be rewritten as (i^5)^20? Then it would be i, no? Why isn't that answer correct?

Note by Michael Reinhard
4 months, 2 weeks ago

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(i^5)^20 = (i^4 * i)^20 = (1 * i)^20 = (i^4)^5 = 1^5 = 1

- 4 months, 2 weeks ago

Thanks! That is very a very helpful explanation, Pi Han.

- 4 months, 2 weeks ago